Analytical Approach to the Determination of Dynamic Characteristics of a Beam With a Closing Crack

Vibration-Based Diagnostics of Fatigue Damage of Beam-Like Structures

“…The present work is a logical continuation of that research [9]. Therefore, the aim of the study is to develop the algorithm of consecutive (cycle-by-cycle) calculation of cracked beam mode shapes amplitudes, to investigate the regularities of concomitant mode shapes origination, and to study the level of non-linear distortions of the displacement, acceleration and strain waves.…”

“…In earlier work [9], the solution of the problem of the bending vibrations of a cantilever beam with a closing crack during the "rst cycle of vibration was described. It was shown that at the instant of crack opening, the so-called concomitant mode shapes di!er from the initially given mode shape.…”

The non-linear dynamic response of the Euler–Bernoulli beam with an arbitrary number of switching cracks

“…In the studies investigating the non linear behaviour the presence of a single crack is usually considered [5,7,[17][18][19][20][21][22][23][24][25], while multiple cracks have been analysed under an harmonic excitation only [26] and by means of a finite element approach. A short comprehensive review of these studies can be found in references [19,26].…”

In-Plane Vibrations of Circular Curved Beams with a Transverse Open Crack

“…Continuous crack theory was developed [18], finite elements and component mode synthesis methods were combined [19], simple methods for frequencies were proposed [20], dynamic characteristics were studied analytically for a closing crack [21], frequencies of multiple cracked beam were calculated by modeling the cracks as a rotary springs [22], dynamic behaviors were presented using strain energies given by linear fracture mechanics theory [23], and FEM was used to calculate natural frequencies [24].…”